{
  "id": "2004.04488",
  "version": "v1",
  "published": "2020-04-09T11:17:00.000Z",
  "updated": "2020-04-09T11:17:00.000Z",
  "title": "On the spectral radius of bi-block graphs with given independence number $α$",
  "authors": [
    "Joyentanuj Das",
    "Sumit Mohanty"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A connected graph is called a bi-block graph if each of its blocks is a complete bipartite graph. Let $\\mathcal{B}(\\mathbf{k}, \\alpha)$ be the class of bi-block graph on $\\mathbf{k}$ vertices with given independence number $\\alpha$. It is easy to see every bi-block graph is a bipartite graph and for a bipartite graph $G$ on $\\mathbf{k}$ vertices, the independence number $\\alpha(G)$, satisfies $\\ceil*{\\frac{\\mathbf{k}}{2}} \\leq \\alpha(G) \\leq \\mathbf{k}-1$. In this article, we prove that the maximum spectral radius $\\rho(G)$, among all graphs $G \\in \\mathcal{B}(\\mathbf{k}, \\alpha)$ is uniquely attained for the complete bipartite graph $K_{\\alpha, \\mathbf{k}-\\alpha}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-09T11:17:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A18"
    ],
    "keywords": [
      "bi-block graph",
      "independence number",
      "complete bipartite graph",
      "maximum spectral radius",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}